=5(2y-1)-y(1-2y)

Solution for =5(2y-1)-y(1-2y) equation:

Simplifying
0 = 5(2y + -1) + -1y(1 + -2y)

Reorder the terms:
0 = 5(-1 + 2y) + -1y(1 + -2y)
0 = (-1 * 5 + 2y * 5) + -1y(1 + -2y)
0 = (-5 + 10y) + -1y(1 + -2y)
0 = -5 + 10y + (1 * -1y + -2y * -1y)
0 = -5 + 10y + (-1y + 2y2)

Combine like terms: 10y + -1y = 9y
0 = -5 + 9y + 2y2

Solving
0 = -5 + 9y + 2y2

Solving for variable 'y'.

Combine like terms: 0 + 5 = 5
5 + -9y + -2y2 = -5 + 9y + 2y2 + 5 + -9y + -2y2

Reorder the terms:
5 + -9y + -2y2 = -5 + 5 + 9y + -9y + 2y2 + -2y2

Combine like terms: -5 + 5 = 0
5 + -9y + -2y2 = 0 + 9y + -9y + 2y2 + -2y2
5 + -9y + -2y2 = 9y + -9y + 2y2 + -2y2

Combine like terms: 9y + -9y = 0
5 + -9y + -2y2 = 0 + 2y2 + -2y2
5 + -9y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
5 + -9y + -2y2 = 0

Factor a trinomial.
(1 + -2y)(5 + y) = 0

Subproblem 1
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {0.5, -5}